Non-semisimple quantum invariants and topological field theories
In this course, we give an introduction to quantum invariants of 3-manifolds and topological field theories associated to non-semisimple tensor categories. The topics of the course include:
1. A brief review on finite tensor categories and Hopf algebras.
2. Lyubashenko's 3-manifold invariant associated to modular tensor categories.
4. Modified trace for tensor ideals.
5. Surgery TFT of De Renzi, Gainutdinov, Geer, Patureau-Mirand and Runkel.
6. Non-compact TFT of Costantino, Geer, Patureau-Mirand and Virelizier.
7. A new open-closed non-compact TFT from universal construction.
1. A brief review on finite tensor categories and Hopf algebras.
2. Lyubashenko's 3-manifold invariant associated to modular tensor categories.
4. Modified trace for tensor ideals.
5. Surgery TFT of De Renzi, Gainutdinov, Geer, Patureau-Mirand and Runkel.
6. Non-compact TFT of Costantino, Geer, Patureau-Mirand and Virelizier.
7. A new open-closed non-compact TFT from universal construction.
讲师
日期
2026年04月08日 至 06月24日
位置
| Weekday | Time | Venue | Online | ID | Password |
|---|---|---|---|---|---|
| 周三 | 13:30 - 16:55 | A3-3-301 | ZOOM 03 | 242 742 6089 | BIMSA |
参考资料
[L] Lyubashenko, V.: Invariants of 3-manifolds and projective representations of mapping class groups via quantum groups at roots of unity. Commun. Math. Phys. 172, 467–516 (1995).
[GKP] Geer, N., Kujawa, J. & Patureau-Mirand, B. M-traces in (Non-Unimodular) Pivotal Categories. Algebr Represent Theor 25, 759–776 (2022).
[DGGPR] De Renzi, M., Gainutdinov, A., Geer N., Patureau-Mirand B., Runkel, I.: 3-Dimensional TQFTs from non-semisimple modular categories. Sel. Math. New Ser. 28, 42 (2022).
Costantino F., Geer N., Patureau-Mirand B., Virelizier A.: Non compact (2+1)-TQFTs from non-semisimple spherical categories. arXiv:2302.04509v3.
[GKP] Geer, N., Kujawa, J. & Patureau-Mirand, B. M-traces in (Non-Unimodular) Pivotal Categories. Algebr Represent Theor 25, 759–776 (2022).
[DGGPR] De Renzi, M., Gainutdinov, A., Geer N., Patureau-Mirand B., Runkel, I.: 3-Dimensional TQFTs from non-semisimple modular categories. Sel. Math. New Ser. 28, 42 (2022).
Costantino F., Geer N., Patureau-Mirand B., Virelizier A.: Non compact (2+1)-TQFTs from non-semisimple spherical categories. arXiv:2302.04509v3.
听众
Advanced Undergraduate
, Graduate
, 博士后
, Researcher
视频公开
不公开
笔记公开
不公开
语言
中文
讲师介绍
王亦龙于2018年从俄亥俄州立大学数学专业博士毕业，之后在路易斯安那州立大学任博士后，并于2021年加入BIMSA任助理研究员。主要研究方向为量子代数与量子拓扑，具体课题包括模张量范畴及其对应的拓扑量子场论的代数与数论性质。